The pair met for key talks over a working dinner at Downing Street on Sunday night, with Tusk, who leads a body made up of the heads of the European Union
's member states, saying beforehand that he would table a proposed deal Monday if an agreement was reached.
But Tusk left the meeting after less than two hours, tweeting that there was "no deal yet" and "intensive work in the next 24" hours was "crucial."
Cameron tweeted that the pair had had a "good meeting," with Tusk having "agreed to another 24 hours of talks before publishing the draft UK renegotiation text."
A Downing Street spokesman said "much progress" had been made, but there were "still areas where there is more to do."
'Emergency brake' on welfare
Cameron is seeking to substantially renegotiate the terms of the UK's EU membership before it holds a referendum on staying in or leaving the European Union -- in what has been dubbed a potential "Brexit," or "British exit" -- later this year.
He is seeking to reach an agreement so the proposal can be put to European leaders at a key summit next month.
The talks with Tusk have addressed four areas of proposed reform, the most pressing of which has been the eligibility of new migrants to the UK to receive welfare benefits, a Downing Street spokesman said.
had presented data that made it clear the UK's current circumstances met the criteria to trigger an "emergency brake" on welfare benefits to migrants from the EU for four years, the spokesman said.
The British Prime Minister was insisting that the emergency brake would kick in immediately after any referendum and "apply long enough to resolve the underlying problem," the spokesman said.
He also said that Cameron believed that the current plans for the brake sketched out so far were not strong enough, and that the measure "should only be a stopgap to a more permanent mechanism."
EU officials have said the brake on welfare benefits -- such as income supplements for those in low-paid work -- should kick in only if the UK can prove that its welfare system is overwhelmed by the burden from migrants.
Public opinion closely divided
Other areas being negotiated include protecting the interests of countries within the European Union that do not use the euro as currency, such as the UK, and closing loopholes exploited by undocumented immigrants.
"We want to see more substantive proposals including closing backdoor routes to Britain which have enabled non-EU illegal migrants to stay in Britain in recent years," the Downing Street spokesman said.
Polls suggest that British public opinion is closely divided on the Brexit question. The latest YouGov poll of 2,438 adults
said that 42% favored leaving the EU, with 38% wanting to remain.
A poll of polls averaging the results of the last six polls
on the issue has found 53% in favor of remaining, and 47% in favor of a Brexit.